I mean for one thing - the placebo effect exists. That's why double blind testing of new drugs is the standard
Saying that wouldn't be useful is kinda like saying HN/Reddit isn't useful because it's all anecdotal, that applies to almost all topics in life.
Lastly, let's not pretend that most doctors do actually follow properly a patient blood before/during/after a course of a drug, in most cases, doctor will just ask How did it go, any side effects?... That's a new "data" for the doc, all anecdotal, almost the same value as a "trusted" rando on Reddit.